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Zbl 0642.53047
Bavard, C.
Courbure presque négative en dimension 3. (Almost negative curvature in dimension 3). (French)
[J] Compos. Math. 63, 223-236 (1987). ISSN 0010-437X; ISSN 1570-5846/e

The following striking theorem is proved: Any closed orientable 3- manifold, M, admits a riemannian metric with curve(M)$\le 1$, diam(M)$\le \epsilon$, and Vol $M\le \epsilon$, for any $\epsilon >0$. The first construction of this kind was given by Gromov in the case $M=S\sp 3$ [cf. {\it P. Buser} and {\it D. Gromoll}, Gromov's examples of almost negatively curved metrics on $S\sp 3$ (to appear)]. In these examples the lower bound for the curvature goes to -$\infty$. This is indeed necessary as was shown recently by Fukaya and Yamaguchi.
[K.Grove]

MSC 2000:: *53C20 Riemannian manifolds (global)

Keywords: diameter; volume; almost negatively curved metrics; curvature

Cited in: Zbl 0651.53032

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